It's a great project, and I hope they manage to ~hem~ pull it off (in seven seconds or less...)
Wood seems to be a scary material for many aircraft builders today, although wheels up's post does delineate some of the very real issues that exist.
Wood remains an excellent material for building aircraft out of, just like every other aircraft construction method, provided you do it properly. It's also one of the few renewable resources we have for the job, and as is often said, it's natures' own composite.
Any modern reproduction or restoration will have to contain some compromises or changes for safety and modern airworthy requirements, but as bdk has shown, you'd probably buy in more re-engineering with a modern composite or substitution as the problems you'd avoid.
I'm talking to restorers building a static DH Mosquito in airworthy and original standards, and we should all be aware of Glynn Powell's work in NZ building new-wood Mosquitoes to fly. (I'm also supporting a project to build a 1914 biplane trainer - of wood, but that's another story.)
It's difficult and expensive, but it's not impossible. And the Mosquito wasn't the most advanced Wooden aircraft by any means. de Havilland Albatross anyone?
Interior:
Yes, the entire main structure, fuselage and wings of the Albatross, a four engine, pre-war airliner was wood. The same wooden sandwich construction of ply-balsa-ply as the later Mosquito. The reverse cycle air cooling of the inverted V engines was innovative as well. It wasn't a perfect design; but it worked perfectly well once they'd got the teething problems out of the way. Show an experienced woodworker a photo of the Albatross and they often won't believe it's wood.
If the challenges of building a wooden aircraft as well as you can seem to encourage replication with modern materials, then you are probably in the wrong game, surely. It's not easy or cheap either way, and a look-alike won't have the merit of authenticity. Why not just make whooshing noises and run around on the ground?

You'd be home for beer or tea earlier, and it's a lot cheaper!
I'm no restorer, but I am very familiar with talking to restorers who run a mile at the mention of wooden construction, and then other rebuilders who have this method as their bread and butter. It can be done.
Just a few thoughts.